What is this extra geometry which cannot be edited in edit mode?
That 'extra' geometry seems to be created by the modifier stack so can't be selected in edit mode unless you apply the modifiers.

I would dare say it actually looks like a face with a wrong normal producing that artifact with a solidify modifier. If that's the case in edit mode select all your geometry and press Ctrl+N to Unify Normals and see if the artifact is gone.

Edit

Your problem are overlapping extra faces, you probably created them accidentally by extruding your faces and inadvertently creating zero sized faces.

Switch to face selection mode by pressing Ctrl + Tab, select and erase the extra zero sized faces by pressing X, then select all by pressing A.
After remove doubles by  access the Specials menu (W) > Remove Doubles et voilá mesh clean.